Fast L1-NMF for Multiple Parametric Model Estimation
This work addresses the problem of robust parameter estimation in computer vision and related fields, offering an incremental improvement with a faster algorithm for existing L1-NMF methods.
The authors tackled the problem of multiple parametric model estimation by developing a parameterless biclustering algorithm based on L1 nonnegative matrix factorization (L1-NMF) that analyzes RANSAC outputs, avoiding spurious inconsistencies and not requiring non-intersecting models. They introduced an accelerated L1-NMF algorithm that handles medium-sized problems faster and extends to larger datasets, with applications beyond this specific context.
In this work we introduce a comprehensive algorithmic pipeline for multiple parametric model estimation. The proposed approach analyzes the information produced by a random sampling algorithm (e.g., RANSAC) from a machine learning/optimization perspective, using a \textit{parameterless} biclustering algorithm based on L1 nonnegative matrix factorization (L1-NMF). The proposed framework exploits consistent patterns that naturally arise during the RANSAC execution, while explicitly avoiding spurious inconsistencies. Contrarily to the main trends in the literature, the proposed technique does not impose non-intersecting parametric models. A new accelerated algorithm to compute L1-NMFs allows to handle medium-sized problems faster while also extending the usability of the algorithm to much larger datasets. This accelerated algorithm has applications in any other context where an L1-NMF is needed, beyond the biclustering approach to parameter estimation here addressed. We accompany the algorithmic presentation with theoretical foundations and numerous and diverse examples.